Sparse estimation of light transport matrix under saturated condition

The Light Transport Matrix (LTM) is a model of the light ray propagation between a projector and a camera. In case of LTM measurement, sparse estimations are often used. They assume the linearity between the projector and camera intensities. Sparse estimation requires multiple projector pixels to be irradiated together. Since multiple projector pixels are irradiated, the camera captures both the direct and global illumination. When the intensity of the illumination received by a camera pixel is higher than the threshold, camera intensity is clipped to the threshold. The camera intensities can be saturated, even if the LTM elements are not saturated, because of the global illumination. This saturation breaks the assumption of sparse estimation and causes the estimated result to be inaccurate. We propose a new sparse estimation algorithm “Saturation ADMM,” which estimates the LTM under conditions in which camera images are saturated because of global illumination. We used numerical simulation and real scene measurement experiments to prove the ability of the proposed method to accurately estimate the LTM under saturated conditions.